Problem 1. Perfect Competition
Consider an industry in which there are 10 identical firms and 1000 identical consumers. Each consumer has the demand function y=1 - 0.005p. Each firm has the following short run cost function: TC(y) = 10y+y2.
a. What is the market demand function?
b. What is each firm's supply function?
c. What is the market supply function?
d. Draw a graph illustrating one firm's as well as the industry's supply function and market demand function. What are the equilibrium price and quantity?
How much each of the firms is producing?
Now suppose the industry has 10 more firms with the cost function TC(y)=20y+y2.
e. What is one of these firm's supply function?
f. What is the market supply function now? What is the new market price?
Problem 2. Perfect Competition
A perfectly competitive industry has a large number of potential entrants. Each firm has an identical cost structure with the long run average cost minimized at an output of 20. The minimum average cost is $10 per unit. Total market demand is Y=1500 - 50p.
a. What is the industry long run supply curve?
b. What is the long run equilibrium price? Total quantity sold on the market? The number of firms on the market? The output of each firm?
The short run cost curve for each firm is C(y) = 0.5y2 -10y+200
c. Derive the average and marginal cost functions. At what output level the average cost is minimized?
d. Derive the short run supply curve for each firm and the short run industry supply with 3 firms on the market.
Problem 3. Monopoly.
The demand for electricity is p = 100 - 2y. (equivalently y = 100 - p)/2).
Suppose the market is monopolized by the producer with the cost function C(y) = 20y
a) derive the marginal revenue and the marginal cost functions
b) equate the marginal revenue and the marginal cost and compute an equilibrium- the price that a monopolist charges and how much does he sell?
c) Write down the profit function Π(y) = R(c) - C(y)
Monopolist chooses as a profit maximizing solution the y where the marginal profit is equal to zero.
d) compute the marginal profit function
e) what is the profit maximizing solution (does it coincide with the one in b) above)
The book says that monopolist can choose either the level of output - y, bearing in mind that his choice of y will affect the market price p, or the other way round: monopolist can choose the price p, this will affect the demand y, but monopolist takes this into account and obtains the same profit maximizing solution.
f) write down the profit function as a function of p, that is profit = (p-MC)y(p)
g) derive the marginal profit as a function of p
h) what is the profit maximizing price (does it coincide with the one in b) above) how much is being sold?